Causal inference

中介分析的目的是评估通过和围绕一些中介的一些暴露对结果的影响。虽然在最近的文献中已经解决了多介质的调解分析，多个曝光的情况下，很少受到关注。在多重暴露的情况下，我们考虑了同时允许变量选择和效应估计的正则化，从而稳定模型拟合并考虑模型的不确定性。在线性结构方程模型的框架下，我们分析表明，两阶段的回归系数正则化的方法并不能保证单峰后验分布，和一个产品的系数的方法，正则化的直接和间接的影响往往会惩罚过度。相反，我们提出了一个正则化的系数差异的方法，是免费的这些陷阱。利用频率论正则化和具有拉普拉斯先验的贝叶斯分层模型之间的联系，我们开发了一种用于后验推理的高效马尔可夫链蒙特卡罗算法。仿真结果表明，该方法具有较好的经验估计性能.该方法说明使用两个数据从生殖流行病学。

Mediation analysis aims at assessing the effect of some exposures on an outcome both through and around some mediators. While multi-mediator mediation analysis has been addressed in recent literature, the case with multiple exposures received little attention. With the presence of multiple exposure, we consider regularizations that allow variable selection and effects estimations simultaneously, hence stabilize model fit and account for model uncertainty. In the framework of linear structural equation models, we analytically show that a two-stage approach that regularizes on regression coefficients does not guarantee unimodal posterior distribution, and a product-in-coefficient approach that regularizes on direct and indirect effects tend to penalize excessively. We instead propose a regularized difference-in-coefficient approach that is free of these pitfalls. Using connections between frequentist regularizations and Bayesian hierarchical models with Laplace priors, we develop an efficient Markov chain Monte Carlo algorithm for posterior inference. Through simulations, we show that the proposed approach has good empirical performance in estimation. The methodology is illustrated using two data from reproductive epidemiology.